The Vertical Line Test

The requirement that each input to a function must produce exactly one output can be used to visually determine when a graph is the graph of a function. Points on the horizontal axis represent the inputs and points on the graph represent input/output pairs. So, if the graph represents a function then a vertical line through any point on the horizontal axis can intersect the graph at most once. This visual check is known as the vertical line test.

Click, or click and drag, in the plots to see the vertical line test applied.